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arXiv · 1002.0680

Some Relations between Divergence Derivatives and Estimation in Gaussian channels

Jacob Binia
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Abstract

The minimum mean square error of the estimation of a non Gaussian signal where observed from an additive white Gaussian noise channel's output, is analyzed. First, a quite general time-continuous channel model is assumed for which the behavior of the non-Gaussianess of the channel's output for small signal to noise ratio q, is proved. Then, It is assumed that the channel input's signal is composed of a (normalized) sum of N narrowband, mutually independent waves. It is shown that if N goes to infinity, then for any fixed q (no mater how big) both CMMSE and MMSE converge to the signal energy at a rate which is proportional to the inverse of N. Finally, a known result for the MMSE in the one-dimensional case, for small q, is used to show that all the first four terms in the Taylor expansion of the non-Gaussianess of the channel's output equal to zero.

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Jacob Binia. 2010-02-03. Some Relations between Divergence Derivatives and Estimation in Gaussian channels. https://arxiv.org/abs/1002.0680

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